Based on the assumption that protons and electrons are body particles, the motion and state of body particle system are investigated in an energy space. Body particles are objects that have only mass and volume. A body particle has three spatial states: position, posture and profile, corresponding to three modes of motion: translation, rotation and vibration. The energies of three modes of particle system constitute a Descartes energy space. The state of object is represented by a state vector in the energy space. The energy space can be divided into three zones and six phases. The three zones dominated by translation, rotation and vibration modes represent the liquid, solid and gaseous state of the object, respectively. There are three parabolic surfaces in energy space, which represent the equilibrium states of the particle system. It is showed that there are two types of phase transitions in energy space, corresponding to that the change of order parameter is equal to 1/2 or less than 1/2. There are a stable equilibrium area and an unstable equilibrium area in each phase, which predicts the transition between the stable state and the excited state within the phase. Strict analysis proves that the number of energy in equilibrium state must be integers. The Planck constant and Boltzmann constant are both scale transformation coefficients of the motion energy.

Assuming that protons and electrons are three-dimensional body particles that have only mass and volume, the volume repulsion can ensure the finiteness of particle density. A scalar potential and a vector potential are constructed respectively with the mass density and the momentum density. A set of particle field equations is derived from the scalar and vector potentials with the help of vector calculus. The equation set is general field equations in three-dimensional flat space, instead of that in four-dimensional curved spacetime. It is shown that the particle field includes gradient field, divergence field and curl field. The gradient field predicts both attraction and repulsion between particles, the divergence field represents the undulation of particles, and the curl field describes the vortex motion of the particles. It is proven that gravitation and electromagnetism both originate from the interaction of body particles. The undulation of pure electronic system represents both gravitational waves and electromagnetic waves. If graviton and photon are regarded as body particles identical to electron, the electrons are the dark matter in the background of the universe.

A theory of cluster ensemble statistics is developed based on the body particle model. Cluster ensemble is a set of temporal snapshots of particle configuration, which is accurately described by a cluster matrix. The partition functions of liquid, solid and gas are calculated in the statistical zones of the energy space, which directly reveals the relationship between the volume and motional energies. The motional energies of liquid, solid and gas are expressed by the statistical correlations of the particle mass, the rotary inertia and the elastic modulus, respectively. Complete energy relations and equations are derived through the statistics of cluster ensemble. Thermodynamic laws and equations can be logically inferred from the theoretical results. Two types of phase transition mechanism are analyzed based on the theory of body particles and the structure of the energy space.

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